1. Field of the Invention
The present invention relates to techniques for matching, registering, combining or correlating two or more images of a body, or a region thereof, at least one of which is obtained by scanning the body with an imaging apparatus. In its particular aspects, the present invention relates to the matching of two or more volumetric images, where the imaged body region exhibits local geometric deformations which are accounted for by an elastic transformation.
2. Description of the Related Art
Combined use of volumetric images obtained from different imaging modalities or from the same modality at different times, or the matching of an image to a standard image, has numerous industrial and medical applications. In the medical imaging field, three dimensional image studies may be obtained from X-ray Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Positron Emitted Tomography (PET), Single Photon Emission Computed Tomography (SPECT) and Ultrasound modalities. In addition, it is a common practice to collect a volumetric image data set as two dimensional image data for each of a stack of slices. However collected, a volumetric image has intensity values or voxels centered at lattice points in a regular 3D grid.
These modalities often provide complementary information, but are generally characterized by different spatial and contrast resolution as well as differences in position, orientation and scale. Furthermore, a standard image might be available for comparison purposes, for example, from a computerized anatomic atlas. Combined use of two or more of such images has potential applications in functional/anatomic correlation, radiation treatment planning, surgical planning and retrospective studies. All such applications require that the images be registered with each other.
Global affine transformations have been applied to register cranial images, where rigid body assumptions are likely to hold, to account for translation, rotation and scaling. Landmark matching techniques result in global polynomial transformations which can correct for nonrigid transformations sufficiently to register the landmarks. However, local deformations cannot be accounted for thereby.
Burr (D. J. Burr, "A Dynamic Model for Image Registration", Comput. Graphics Image Process. 15, 1981, 102-112) proposed a process of automatic registration of deformed two dimensional images wherein nearest neighbor vectors at each point in one image are defined by connecting that point to the most similar point in a square neighborhood in the other image, which are subjected to a Gaussian cooperative smoothing. Such an approach is not useful for medical gray scale images because of the absence of strong local correlations in intensity patterns. Burr (D. J. Burr, "Elastic Matching of Line drawings", IEEE Trans. Pattern Anal. Mach. Intelligence, PAMI-3, No. 6, 1981, 708-713) also proposed elastic matching of line drawings, made up of points alternating with connecting line segments, using feature displacement vectors directed from points on one line drawing perpendicularly to the nearest line segment on the other line drawing, which I hereafter refer to as "Burr's algorithm". Smoothing of the field of feature displacement vectors is accomplished by elasticity in the line images. Burr's algorithm has also been used for elastic interpolation between contours in two successive serial cross sections (W. C. Lin et al., "Dynamic elastic interpolation for 3-D medical image reconstruction from serial cross sections, IEEE Trans. on Medical Imaging, 7, No. 3, September 1988, 225-232).
Broit and Bacsy (R. Bacsy et al., "Matching of deformed images", Proceedings of the VIth International Conference on Pattern Recognition, Munich, 1982, pp. 351-353) reported a two dimensional model-based object matching approach through elastic deformation, where matching is formulated as a minimization problem with a cost functional that combines a deformation model and a similarity measure. The deformation model involves the strain energy of a globally smoothed elastic body. This approach was later extended to three dimensions by Bajcsy and Kovacic (R. Bacsy et al., "Multiresolution elastic matching", Computer Vision, Graphics, and Image Processing, 46, 1989, pp. 1-21).
I have previously reported (M. Moshfeghi, "Multimodality Image Registration Techniques in Medicine", Proc. IEEE Engineering in Medicine & Biology Society 11th Annual International Conference, 1989, pp. 2007-2008 and M. Moshfeghi, "Elastic Matching of Multimodality Medical Images", CVGIP: Graphical Models and Image Processing, Vol. 53, No. 3, May 1991, pp. 271-282) a two dimensional local registration method involving extracting and matching corresponding contours by iteratively warping a candidate contour from an image to be elastically deformed onto a goal contour from a reference image using an extension of Burr's algorithm. Point pair correspondences between the candidate and goal contours are used to determine local displacement vectors applied to points along the candidate contour. Residual local displacement vectors remaining after subtraction of global image shift are then interpolated onto the entire image using a weighting function which decays asymptotically to zero for large distances. The need was then noted by me to extend the algorithm to 3D, so as to use elastic deformation of corresponding surfaces. That extension of my prior work is the subject of this application.